have no science have the ideas of things more perfect than such as are raised by definitions. As who is there that understandeth not better what a straight line is, or what proportion is, and what many other things are, without definition, than some that set down the definitions of them. But their use is, when they are truly and clearly made, to draw arguments from them for the conclusions to be proved. And therefore you that in your following censures of my geometry, take your argument so often from this, that a point is nothing, and so often revile me for the contrary, are not to be allowed such an excuse. He that is here mistaken, is not to be called negligent in his expression, but ignorant of the science. In the next place, you take exceptions to my definition of _equal bodies_, which is this: “_Corpora æqualia sunt quæ eundem locum possidere possunt_. Equal bodies are those which may have the same place.” To which you object impertinently, that I may as well define a man to be, _he that may be prince of Transylvania_, wittily, as you count wit. Formerly in every definition, you exacted an explication of the essence. You are therefore of opinion that the possibility of being prince of Transylvania is no less essential to _a man_, than the possibility of the being of two bodies successively in the same place, is essential to _bodies equal_. You take no notice of the twenty-third article of this same chapter, where I define what it is we call essence, namely, that accident for which we give the thing its name. As the essence of a man is his capacity of reasoning; the essence of a white body, whiteness, &c., because we give the name of _man_ to such bodies as are capable of reasoning, for that their capacity; and the name of _white_ to such bodies as have that colour, for that colour. Let us now examine why it is that men say bodies are one to another equal; and thereby we shall be able to determine whether the _possibility of having the same place_ be essential or not to _bodies equal_, and consequently whether this definition be so like to the defining of a man by the _possibility of being prince of Transylvania_ as you say it is. There is no man, besides such egregious geometricians as yourselves, that inquireth the equality of two bodies, but by measure. And for liquid bodies, or the aggregates of innumerable small bodies, men (men, I say) measure them by putting them one after another into the same vessel, that is to say, into the same place, as Aristotle defines place, or into the space determined by the vessel, as I define place. And the bodies that so fill the vessel, they acknowledge and receive for equal. But though, when hard bodies cannot be so measured, without the incommodity or trouble of altering their figure, they then enquire, if the bodies are both of the same kind, their equality by weight, knowing, without your teaching, that equal bodies of the same nature weigh proportionably to their